Why is part of mesh deformed by IK Constraints
Switching the pole angle to -90 alone will result in the leg bending backwards and breaking knee caps when you play back the animation. To fix that, I added a Limit Rotation Constraint above the IK Constraint for each leg. I found Rotation Limit values (differing for each leg) that allows the frames of animation to look correct without the mesh distorting or bones bending in the wrong direction:


Uploaded the edited .blend here:

This seems like a quick fix, and I would love to hear more experienced rigger tell some preventative measures that you could take to avoid IK twisting issues in Blender.